3. New Evaluation Method of Building Collapse Risk Compatible with Actual Damage
Ratio
3. 1 Modifications to the Method of TMG
The above-mentioned study indicated the way to modify “building collapse risk” as an
index that reproduces the actual severe damage ratio of buildings in Nada Ward due to the
Kobe Earthquake. First, in equation (1), " D
k: the number of buildings per 1 km 2 " is replaced
by "N
k: the ratio of buildings with category k in number". By this, the building collapse risk
which reproduces the severe damage ratio can be obtained. Next, the weights used in equation
(1) were examined. In the method of TMG, the weights for the seismic resistance of buildings
and the site condition are simply multiplied when evaluating the collapse risk. However, the
collapse risk may be affected by the both parameters at the same time. Hence matrix-type
weights should be introduced to consider the joint effect of the building resistance and the site
condition (intensity of strong motion) on the collapse risk.
3. 2 Method of New Building Collapse Risk Evaluation
A new building collapse risk evaluation method is proposed in this study. In the
proposed method, "Pi: the building collapse risk" is defined in the following equation as an
index instead of "the amount of risk" in the method of TMG.
in which k is the building category (1-14), l indicates the subsurface soil condition (1-4), Nk is
the ratio of buildings with category k in number, Wkl is the matrix-type weight for building
category k and soil condition l. Classifying the collapse risk into 5 levels, a risk level of each
block is obtained. By this equation (3), the effect of the building density is removed from the
collapse risk evaluation, and more realistic risk that represents the building characteristics and
site condition of an area can be calculated.
3. 3 Reliability Analysis to Obtain Damage Probability
In order to make the proposed method applicable to other areas in Japan, the
matrix-type weights were determined by the basic reliability analysis theory. The
vulnerability functions (fragility curves) of 14 building categories for severely damaged
buildings developed by Murao and Yamazaki (2000) were used as the resistance of buildings.
The values of the two parameters of the log-normal distributions are listed in Table 1.
Figure 2: Probability density function of the estimated PGV in the 1995 Kobe Earthquake
for different topographical conditions in Nada Ward
Figure 2 shows the probability density functions of the estimated PGV in the Kobe
Earthquake for different topographical conditions in Nada Ward. These functions were also
obtained by a statistical analysis of the estimated PGV values in Nada Ward and the values of
their parameters are shown in Table 1. The PGV value is widely distributed for mountain and
alluvial fan while the range is comparatively narrower for terrace and delta. But, of course,
this observation is the case for Nada Ward in the Kobe Earthquake. It is necessary to assume
these functions when applying to other areas.
Using the basic reliability analysis theory, the probability for severe damage Pf,which
is the function of the matrix-type weights, is obtained by the following equation:
Pf = P (R/S<1) = 1-F(l
z/xz) (4)
in which R is the seismic resistance of buildings, S is the strong motion index (e.g. PGV),
Fis
the cumulative probability of the standard normal distribution,
lz=
lr -
ls,
and
xz =
(
xr2 +
xs2 )
1/2 , assuming independence between R and S. Using this equation, the weights for the
building collapse risk can be calculated and the values are shown in Table 1. Figure 3(a) plots
the comparison of the weights for the building collapse risk evaluated by equation (4) and the
severe damage ratio observed in the Kobe Earthquake. It is seen that the obtained weights are
compatible with the actual severe damage ratio. The building collapse risk of Nada Ward
calculated by this method is plotted in Figure 3(b). Comparing this figure with the distribution
of severe damage ratio in Figure 1(b), they look quite similar. Thus, it is conducted that the
severe damage ratio was almost reproduced by the proposed method.
Table 1: Parameters of the probability density functions and obtained weights
that reproduce the severe damage ratios due to the Kobe Earthquake
|
| lr
| xr
| Mountain
| Terrace
| Alluvial
Fan
| Delta
|
| -
| -
| 1
| 2
| 3
| 4
|
| ls
| -
| -
| -
| 3.90
| 3.95
| 4.76
| 4.74
|
| xs
| -
| -
| -
| 0.53
| 0.24
| 0.33
| 0.15
|
| Wooden
| -1951
| 1
| 4.36
| 0.41
| 24.6
| 19.5
| 77.9
| 80.8
|
| 1952-61
| 2
| 4.44
| 0.35
| 19.8
| 12.6
| 74.8
| 78.3
|
| 1962-71
| 3
| 4.45
| 0.34
| 19.1
| 11.6
| 74.6
| 78.2
|
| 1972-81
| 4
| 4.73
| 0.38
| 10.1
| 4.1
| 52.7
| 51.0
|
| 1982-94
| 5
| 5.12
| 0.50
| 4.6
| 1.7
| 27.5
| 23.1
|
| RC
| -1971
| 6
| 5.12
| 0.65
| 7.1
| 4.4
| 31.0
| 28.2
|
| 1972-81
| 7
| 5.33
| 0.58
| 3.4
| 1.3
| 19.7
| 16.1
|
| 1982-94
| 8
| 6.01
| 0.79
| 1.3
| 0.6
| 7.3
| 5.8
|
Steel
Frame
| -1971
| 9
| 4.64
| 0.62
| 18.2
| 15.0
| 57.0
| 56.2
|
| 1972-81
| 10
| 4.97
| 0.49
| 6.8
| 3.0
| 36.1
| 32.4
|
| 1982-94
| 11
| 5.64
| 0.73
| 2.7
| 1.4
| 13.7
| 11.3
|
Light
Gauge
Steel
Frame
| -1971
| 12
| 4.70
| 0.55
| 14.8
| 10.7
| 54.2
| 53.1
|
| 1972-81
| 13
| 5.82
| 0.97
| 4.1
| 3.1
| 15.2
| 13.6
|
| 1982-94
| 14
| 6.19
| 1.10
| 3.1
| 2.4
| 10.8
| 9.7
|
(a)
(b)
Figure 3: (a) Comparison between the actual severe damage ratio and the evaluated severe
damage probability; (b) The proposed building collapse risk of Nada Ward
